第24~27届北京市高中力学竞赛决赛汇编.pdf

1、 第24届北京市高中力学竞赛决赛试题 （北京四中杯） 时间120分钟 满分150分 g1078g573g3745g12464g20174g948g25g4677g20174g952g8709g4677g20174g28g2108g952g1959g24g23g2108g949g31. g4018g33741g6256g12138g712g1072g7785g19375g13603g5852g2618g3416g4554g9473g17822g11444g1108g1495g712g1411g18429g11560g2620g11444g11106g451g1161g1108g1258g2102

2、g2139g6339g1407g13603g11444g1072g12575g712g11106g17627g1411g15498g5473g2586g14125g13143g13143g6339g1407g13603g1085g7022g712g1161g17627g1411g5482g3870g14125g11096g2251g10405g5445g14362g5153g8943g13603g2625g1082g10332g15996. g13567g17911g1072g8677g7206g19492g712g1161g1082g2423g11444g20744g5334g1130hg7

3、12g3416g17929g8677g7206g19492g1973g11106g1082g2423g11444g20744g5334_g708g3739g4671g1214g451g12665g1214g6214g3927g1214g709hg712g2511g3344g7263 . 2. g4018g3374 2 g6256g12138g712g1072g1114g5481g12887g12320g1082g12575g3370g4554g712g1083g12575g11096g1072g7785g12550g11556g13551g2625g1083g6393g5481g12887g1

4、2308g712g13551g1083g12575g3370g4554g712g5481g12887g12308g12138g7072g11304N. g4018g7628g5481g12887g12308g1083g12575g5852g2618g1072g18429g11301Ng11444g18429g10393g712g2121g5481g12887g12308g12138g7072g1130_Ng712g10806g11105g7263_ _. g33741 g33742 g33743 3. g1108g1114g10393g1411g2612g18429 1mg2748 2m g7

5、12g11096g1085g2591g1384g19375g13603g17934g6613g712g8596g13603g17432g17911g1072g4554g9473g17822g712g9473g17822g2426g5556g1130r.g4018g33743g6256g12138g712g5424g4091g7206g712g1108g10393g1411g20744g5334g5150hg712 2 1m m g452g1085g16849g9473g17822g17240g18431g2748g6809g6934.g11105g19849g8594g18426g7022g7

6、12g19486g1108g10393g1411g17902g2144g2620g1072g20744g5334g6256g19760g7206g19492_. 4. g4018g33744g6256g12138g712g1278g2620g1072g20744g5334g11444Ag451Bg3892g3506g1083g1108g7785g19375g5334g11560g2620g11444g13603g712g13603g1083g12575g2102g2139g12553g7481g17240g18431g11560g2620g11444g11106g451g1161g1108g1

7、258g712g11106g7153g11444g13603g2591g16852g1130g1085g2591g1384g19375g712g1161g7153g11444g13603g7481g7230g7278g11444g5481g5719g712g5507g1108g1258g2102g2139g8943g13603g10332g2144Ag451Bg3892g7206g712g8708g17843g1108g1258g1674g2255g11444g3914g4673g11444g13571g16874g7263_,g10806g11105g7263_. 5. g6209g1308

8、g2591g17921g1388g16852g1130g3424g10803g13573g3930g19555g1674g2352g17999g3382g2712g17920g2264g712g7480g10803g13573g3424g10803g1674g2352g17999g3382g2712g17920g2264g712g4531g1308g11444g17920g2264g17816g17961g3416g2620g1072g1114g19858g1082g712g1301g3930g19555g1130g2546g13875g13099g712g7480g10803g11444g1

9、7920g2264g17816g17961g2591g12999g11157g11115g6208g4018g33745g6256g12138g11444g15498g13551g712g17929g12285g11115g8965_ g708g3739g8595g11934g6214g19273g16927g709g712g10806g11105_. m2 m1 h g11106 g1161 g11106 A B g1161 g33744 g3930g19555 g7480g1246 g3424g10803 g33745 6. g4018g33746g6256g12138g712g19375

10、g1130Lg11444g1072g8677g13558g13551g712g1072g12575g3370g4554g3416g1913g9473g8804g5283g19858g1082g11444Og9961g712g2582g1072g12575g7747g1407g1072g17240g18431g1130mg11444g4671g10393g1411. g5424g4091g7206g712g10393g1411g17421Og9961g1130bg712bg950Lg712g13577g10393g1411g1072g1114g2125g17999g5334 0v g712g51

11、54g11797. g5507g10393g1411g17920g2264g2144g17421Og9961g1130Lg7206g13551g13607g13143g712g10393g1411g13573Og9961g1674g2426g5556g1130Lg11444g3382g2712g17920g2264g712g8596g7206g13551g11444g5456g2251g12665g1214 _. g1218g573g16855g12749g20174g948g1959g28g25g2108g949g37. g70815g2102g709g5852g14322g7654g114

12、44g12575g18200Ag2748Cg3892g7481g3975g10719g712g5792g4013g3975g3416g19189g3506g11444g3382g7713g1082g712g2591g1301g1082g1083g12331g2264. g4018g7628g3416ABg1082g1420g11096g19189g3506g2251Fg712g4018g33747g6256g12138g712g5507Fg12267g5424g3382g7713g17843g17932g7206g712g5852g14322g7654g4662g16091g3382g7713

13、g1082g11444g6809g6934g2251g2449g1407g13884g1085g14125g12331g2264.g16878g3975g10719g1086g3382g7713g19492g6809g6934g13099g7072g3447g1130g712g7654g18429g1085g16849g712g8818g726g5852g14322g7654g1085g14371g1214g16091g2449g1407g7206g712g19189g3506g2251Fg12267g3382g7713g11444g7472g3927g17421g12267x. 8.g708

14、18g2102g709g5481g5719g10803g14362g20744g3892hg14362g11105g14957g3416g8804g5283g3424g7599g1082g712g10803g1278g3424g7599g1082g5481g17319g2552g3506g11556g14957g1083g712g17929g7783g13591g13597g5481g17443. g4018g7628g8703g8529g12000g6862g2173g11740g19492g17999g5334vg712g12000g2622g11740g19492g17999g5334g

15、1130 vvv =-k (0g950kg9501) . g8818g5481g5719g10803g15996g17312g11444g17439g12347g452g708g12458g8772g19563g2251g1085g16849g709 9.g70818g2102g709g1072g4671g10803g7116g2625g1082g6347g2090g712g6347g2090g11444g2125g17999g5334g1086g8804g5283g7145g2625g11444g3945g16386g1130g712g13567g17911g1072g8677g7206g1

16、9492g1405g12331g1086g8804g5283g7145g2625g3945g16386g1130g712g17999g5334g1086g8804g5283g7145g2625g11444g3945g16386g1130g712g1085g16849g12458g8772g19563g2251g712g2121g1086g451g1147g19492g11444g1955g13099g16024g17902g5439g7263g1264g1144g731 g3374 6 O x a b A C B F g33747 10.g70820g2102g7092011g52843g74

17、8011g7189g7189g7516g2561g110879g13527g3927g3424g19767g712g3424g19767g5445g2561g9127g2984g712g4652g14372g12223g4811g7784g11109g12553g2561g11087g7784g8948g9535. g3416g7784g8948g9535g1117g712g7481g3339g12285g7022g4660g5719g2620g1405g13136g7263g4649g1258g1411g8708g17843g7481g2465g19609g11444g726g11976-1

18、31g451g19231-137g451g19302-90g451g19146-239. g4531g1308g7022g2090g20744g14125g18431g12994g4480g1354g4649g1258g1411g18000g6208g1364g4579g712g4652g14372g1258g1411g13558g14094g11388g2568. g1258g1411g13558g14094g2591g1301g11579g1420g17240g18431g1130 Mg11444g4671g10803g712g1108g13558g14094g19492g11444g19

19、246g6613g10393g2591g11579g1420g17835g7542g708g16878g19375g5334g1130lg709g712g4018g33748g6256g12138. g5507g17240g18431g1130mg11444g20744g14125g12994g4480g1301g17999g5334vg3506g11556g1214g19246g6613g10393g4660g2625g1258g1411g13558g14094g712g1086g13558g14094g2561g11087g8595g12000g5286g11145g3416g13558g

20、14094g18428g7206g712g5677g11157g1258g1411g1958g4531g1323g1413g5537g2813g712g16901g8818g1108g13558g14094g11444g17920g2264g16372g5563g2748g19246g6613g10393g2567g2251g3927g4671. 11.g70825g2102g709g7481g1072g20167g17240g18431g1130mg11444g4671g7247g1411A. g3364g13573g7680g17240g18431g1130Mg712g2426g5556g

21、1130Rg11444g3927g7247g1411g1420g2426g5556g11302Rg11444g3382g2712g17920g2264. g1278g17932g3892g20238g7573g1072g17999g5334g1130 RGMv= g451g17240g18431g11302mg11444g7247g1411Bg1086Ag7247g17918g19858g2561g11087g2199g9976g8595g12000g2622g5522g6208g1072g1114g7136g11444g7247g1411C. g1655g4554g12000g6862g21

22、73g2622g1405g13726g7514g2561g11087g2568g2374. g7081g709g16935g17994g17911g16849g12743g2132g7133g7136g11444g7247g1411Cg7263g2646g1354g1086g3927g7247g1411g2561g11087g12000g6862. g7082g709g4018g7628Bg7247g1278Ag7247g14076g19858g5792g4013g8943g11632Ag7247g11444g17920g2264g7145g2625g17965g1082g4531g5286g

23、2561g11087g1082g17952g12000g6862g712g16935g17994g17911g16849g12743g2132g7133Cg7263g2646g1354g1086g3927g7247g1411g2561g11087g12000g6862. vm, M g33748 第24届北京市高中力学竞赛决赛试题参考答案 （北京四中杯） g1078g573g3745g12464g20174g31. g12665g1214g727g13603g4649g11106g451g1161g1108g1258g11444g6393g2251g3927g4671g11560g12665g

24、452 2. 4Ng727g13551g19375g5334g2561g11087g5598g4671g13657g11805g712g13551g6393g2251g2047g4671g11303Ng452 3. 1 22 1( )( )M M hhta M M g+= = 4. g1108g1258g1674g11444g2255g11560g12665g727g11106g1086g13603g451g1161g1086g13603g11444g2090g7515g10470g5681g11560g2620g712g13603g11444g5481g5719g1085g5537g2813

25、g1161g1674g2255g3914g4673g452 5. g19273g16927g727g3930g19555g4649g7480g10803g11444g5445g2251g5739g8708g3424g10803g4649g7480g10803g11444g5445g2251g3927g712g1301g3930g19555g1130g2546g13875g13099g712g7480g10803g11444g17920g2264g17816g17961g5739g7263g2088g5522g11444g452 6. 2 2 203sinmv bl g1218g573g1685

26、5g12749g20174g37. g16403g726g16878xg1130g1124g11132g10470g5681g7206g11444g17421g12267 g2251g5283g16017 0C AN N = g7081g709 0A Cf f F+ = g7082g709 g2251g11801g5283g16017Ag1130g2546g13875g9961 02C C aN b f a F X + + = g7083g709 A Af N= C Cf N= g13956g12539g726 2bX = g6256g1301 2bX 8. g16403g726g12636g

27、1072g8529g12000g6862g11740g19492g17999g5334 1 2v mh= g12000g6862g2622g17999g5334 1 1 2v mh= g452h1g1130g5481g17319g11444g20744g5334g452 g6256g1301 1h k h= 21h k h= g12636g1212g8529 2 42 1h k h k h= = g12636Ng8529 2 21 nn nh k h k h= = g6256g1301 ( )2 2 41 22 2 2 2 1 nS h h h h h k h k k= + + + + + =

28、 + + + + 2 22 22 11 1k h kh hk k+= + = NA fA A x F B b a C NCfC 9. g16403g726g4671g10803g11444g17920g2264g5877g2021g4018g3374g6256g12138g712g2591g5575 0 cosx vt = 0sin sin2v vy t += 0sin sintan 2cosv vyx += = g2552g7481 0cos cosv v = g6256g1301tan 2tan tan = 10. g16403g726g16878g19246g6613g10393g193

29、75g1130l g5677g11157g1258g1411g1958g1286g1323g1413g5537g2813g712g12000g6862g7206g2264g18431g4536g5762g712g7481g726 ( )2 Cmv M m v= + g5439g1117vCg1130g17240g5619g11444g17999g5334g712g11105g8596g5575g726 2Cmv vM m= + g7145g2625g1086vg11560g2620g712g6256g1301g13099g13583g11444g17240g5619g1301 2C mv vM

30、 m= + g11444g17999g5334g1674g2352g17999g11556g13551g17920g2264g452g11105g1214g7076g1114g13099g13583g4649g17240g5619g8913g7481g3910g2251g11801g1420g11096g712g7029g13099g13583g4649g17240g5619g11444g16386g2264g18431g4536g5762g712g2467g726 ( )2 22 1 2mvx Mx M m x = + + g1958g1117 2 2 Mlx M m= + g727 1 2

31、M mx lM m+= + g712g2102g2139g1130g12000g6862g2622g2595g17897g4671g10803g2748g5142g17897g4671g10803g2144g17240g5619Cg11444g17421g12267g452 ( )2 222 2 2Ml M m Mmv M M m lM m M m M m + = + + + + + g5439g1117g1130g1108g13558g14094g4649g17240g5619g11444g16386g17999g5334g712g2467g1108g13558g14094g13573g17

32、240g5619g1674g2352g17999g3382g2712g17920g2264g712g2620g7206g17240g5619g1674g2352g17999g11556g13551g17920g2264g452 ( )mvM m l= + g19246g6613g10393g2567g2251g3927g4671g1130g726 ( ) ( )( )2 22 2 2Ml Mm vT M m M m l M m M m = + = + + + 11. g16403g726Ag7247g17920g2264g11444g17999g5334 1 2GMv R= g7081g709

33、g12000g6862g2199g9976g712g2264g18431g4536g5762g726 1 22 3mv mv mv = g708v2g1130Cg7247g17999g5334g709 2 1 2 23 2GMv R= Cg7247g11444g14125g18431 ( ) ( )22 3 3132 2 2 1.2k p GM m GM mE E E mv R R= + = = M l mg712v v0 r y v x c g7785g6558Eg7280g712g6256g1301g17816g17961g1130g8029g3382g452 g2552g7785g655

34、8g14125g18431Eg1086g8029g3382g2426g19375g17828ag11444g1955g13099 ( )32GM mE a= g712g6256g1301 1.2a R= g452g5522g6208Cg7247g11444g17319g4091g1405g13726g1130g8029g3382g11444g17932g3424g9961g712g2132g7133g7263g2646g1086g3927g7247g1411g11560g12000g712g11579r Rg24338 g452g10720g3416rg17921 = 2a-rg17932 =

35、 2.4R-2Rg728Rg712g7029g1072g4554g11560g12000g452 g7082g709g12000g6862g2199g9976g712g2264g18431g4536g5762g726 1 22 3mv mv mv+ = g708v2g1130Cg7247g17999g5334g709 2 1+2 23 2GMv R= Cg7247g11444g14125g18431 ( ) ( )22 3 3132 2 2 5.4k p GM m GM mE E E mv R R= + = = g7785g6558Eg7280g712g6256g1301g17816g1796

36、1g1130g8029g3382g452 g2552g7785g6558g14125g18431Eg1086g8029g3382g2426g19375g17828ag11444g1955g13099 ( )32GM mE a= g712g6256g1301 5.4a R= g452g5522g6208Cg7247g11444g17319g4091g1405g13726g1130g8029g3382g11444g17921g3424g9961g712 =2r R Rg24338 g712g6256g1301g1072g4554g1085g1354g2561g11087g12000g6862g45

37、2 g19246g6613g10393g2567g2251g3927g4671 ( ) ( )( )2 222 2Ml Mm vT M mM m l M m M m = + = + + + O R 2R 第25届北京市高中力学竞赛决赛试卷 （北京四中杯） g1078g573g3745g12464g20174g9486g4677g20174g952g8709g4677g201748g2108g952g195948g2108g949 1. g1072g17443g17932g17920g2264g2696g3416g3424g10803g16024g19858g17443g17932g712g17

38、319g17443g7206g17999g5334g113010m/sg712g14125g17443g20907.5mg17932. g5154g11797g7480g10803g16024g19858g11444g18429g2251g2256g17999g5334g7263g3424g10803g16024g19858g18429g2251g2256g17999g5334g114441/6g712g4018g7628g1286g3416g7480g10803g16024g19858g17443g17932g712g17319g17443g17999g5334g3927g4671g1167

39、g726310m/sg712g1286g17443g17932g11444g16864g5509g4662g7263 m. 2. g1072g1134g18429g17920g2264g2696g14125g1134g17319100kgg11444g18429g10393g712g1286g4649g1072g7785g13805g8715g14125g7149g22561000Ng11444g2251g2631g731 g12676g726 g712g10806g11105g7263 . 3. g4374g4181g20238g14441g13573g7480g10803g1674g235

40、2g17999g3382g2712g17920g2264g712g9083g2090g1958g2712g7503g1130Tg712g2121g20238g14441g17421g7480g10803g16024g19858g11444g17421g12267g1130hg712g2591g2646g1085g16849g3424g10803g5445g2251g13884g17921g1388g16024g17952g11302324GMTh R= g712g1958g1117 M g7263g7480g10803g11444g17240g18431g712R g7263g7480g108

41、03g2426g5556. g12676g726 g712g10806g11105g7263 . 4. g6558g2375g1244g7306g63572012g52843g748017g7189g2748g2546g13875g9144g57913g748018g7189g6357g18051g712g3989g3424g2137g2295g3867g21181g4086g2256g6449g13539g12782.18g1079g12963g20744g12458g11444g8790g8772g10803g2618g12830g1117g17395g1083g712g1083g1495

42、7g11444g7472g20744g17999g5334g2144163m/s.g1083g14957g135263g210243g12290g712g17421g3424g198582400mg20744g3892g6275g5424g1358g712g7076g1114g1083g14957g2144g3424g19858g11444g7206g19492g6449g135978g21028g12290. g16901g7785g6558g6357g13544g6357g18051g2748g1424g11444g2102g7616g712g3416g33741g1117g8708g17

43、843g2038g11934g3424g11115g2090g3989g3424g2137g2295g3867g1083g14957g2144g3424g19858g17911g12347g11444v-tg3374g13551. 175 150 125 100 75 50 25 O 60 120 180 240 300 360 420 480 t / s v / mg103s-1 g33741 5. g1083g19736g3929g712g1655g16878g7184g20222g712g19736g9508g1301g17999g5334v1g12550g11556g1083g1495

44、7g712g19736g9508g3416g12458g1117g11444g2102g5171g7263g3447g2352g11444g712g2437g1405g1411g12319g11444g19736g18431g7263. g4018g33742g6256g12138g712g1072g1114g1258g16305g1278Ag3892g17920g2264g2144Bg3892g712g1286g8913g7481g5206g1358g712Ag451Bg11444g17421g12267g1130lg712g1258g11444g17920g2264g17999g5334g

45、1130v2. g6330g1258g12720g2374g1130g19375g7145g1411g8273g3515g712g3940g2748g14041g11444g8804g5283g19858g12319g1130S1g712g17627g1411g2173g7145g8595g19858g11444g12550g11556g19858g12319g1130S2. g2121g1258g1278Ag2144Bg17911g12347g1117g712g6275g2144g19858g12319S1g1082g11444g19736g18431g1130 g712g6275g2144

46、g19858g12319S2g1082g11444g19736g18431g1130 . 6. g1081g1114g17240g18431g3447g1130mg11444g4671g10803Ag451Bg451Cg712g11096g17835g7542g17934g6613g712g4018g33743g6256g12138. Ag451Bg1086Bg451Cg11444g17421g12267g11560g12665g712Ag451Bg451Cg1086g3424g10803g1117g5619Og3416g1072g7569g11556g13551g1082. g1081g11

47、14g4671g10803g3416g20744g12458g13573g3424g10803g1674g2352g17999g3382g2712g17920g2264g712g4018g7628g17835g7542g7014g2144g6304g2264g13884g1663g12267g11556g13551g1072g4671g16386g5334g712g2121g17835g7542g1086g11556g13551g11444g1663g16386g4662 g708g3790g3927g451g2047g4671g451g1085g2568g709g712g10806g1110

48、5g7263 .g708g7516g20168g16932g7230g6615g2150g2459g7247g3929g13551g5739g6455g2625g3424g10803g11444g3626g7516g2511g10806g709 g1218g573g16855g12749g20174g948g1959g20g19g21g2108g949g37.g70816g2102g709g1108g1114g11560g2620g11444g2426g10803g712g2426g5556g18221g7263rg712g17240g18431g11300.5mg712g7022g3416g19849g6809g6934g3344g7072g1130 = 0.5g11444g8804g5283g19858g1082. g3416g1108g1114g2426g10803g1082g7022g1072g1114g2426g55